LaRC02 failure analysis (2D)

LaRC02 failure theory NOTE applies to unidirectional fibers. There are two different LaRC02 failure criteria:

• Fiber failure criterion — In this criterion, three mutually exclusive fiber failure criteria equations are developed. One equation is used if fibers fail under tension and the other two equations are used if fibers fail under compression. For fiber compression, a misalignment plane is assumed and different equations are used depending on whether the misalignment normal matrix stress is tensile or compressive, σm2.

• Matrix failure criterion — In this criterion, three mutually exclusive matrix failure criteria equations are developed. One equation is used if the matrix fails under tension and the other two equations are used if the matrix fails under compression. For matrix compression, different failure index equations are used depending on the size of the normal fiber stress, σ1, with respect to the compressive stress allowable in direction 2 of the unidirectional ply, YC.

Fiber failure under tension

The fiber fails under tension when the following formula is true:

σ1 ≥ 0

In this case, the failure criterion is the same as the failure criterion of the maximum strain failure theory.

Failure Index

• The expression for the fiber failure index, Ff is:where XTε is the tensile strain allowable in direction 1 of the unidirectional ply.

Margin of Safety

• The margin of safety for the fibers calculated as a percentage, MSf, is:

Strength Ratio

• The fiber strength ratio, SRf, is:

Fiber failure under compression

The fiber fails under compression when the following formula is true:

σ1 < 0

Failure Index

• To calculate the fiber failure index in the case of fiber failure under compression, a fiber misalignment plane is assumed. Two cases exist. If the misalignment normal matrix stress is tensile, σm2 ≥ 0, then the expression for the fiber failure index, Ff is:If the misalignment normal matrix stress is compressive, σm2 < 0, then the expression for the fiber failure index, Ff is:whereThe stresses are defined in the misalignment plane as follows:YT is the tensile stress allowable in direction 2 of the unidirectional ply.S is the shear strength of the unidirectional ply given by: S = YC/2.G12 is the shear modulus.XC is the compressive stress allowable in direction 1 of the unidirectional ply.α0 is the maximum possible fracture angle due to transverse compression and shear. In scientific literature, it is defined as 53°. This is the value used by this software.The < > operator is called the MacLaurin operator, and is defined as:

Margin of Safety

• The margin of safety for the fibers calculated as a percentage, MSf, is:

Strength Ratio

• The fiber strength ratio, SRf, is:

Matrix failure under tension

The matrix fails under tension when the following formula is true:

σ2 ≥ 0.

Failure Index

• The expression for the matrix failure index, Fm is:

Margin of Safety

• The margin of safety for the matrix calculated as a percentage, MSm, is:

Strength Ratio

• The matrix strength ratio, SRm, is:

Matrix failure under compression

The matrix fails under compression when the following formula is true:

σ2 < 0

Failure Index

• To calculate the matrix failure index in the case of matrix failure under compression, two cases exist.If the normal fiber stress is larger than or equal to the compressive stress allowable in direction 2, σ1 ≥ YC, then the expression for the matrix failure index, Fm is:If the normal fiber stress is smaller than to the compressive stress allowable in direction 2, σ1 < YC, then the expression for the matrix failure index, Fm is:whereThe effective transverse and longitudinal stresses are:The effective transverse and longitudinal stresses in the fiber misalignment plane are:α is the fracture angle due to transverse compression and shear. This angle is determined by looping over all angles between 0 < α < α0 and finding the α angle that gives the maximum matrix failure index, Fm NOTE.Fiber directionFracture of a unidirectional ply subjected to transverse compression and shear

Margin of Safety

• The margin of safety for the matrix calculated as a percentage, MSm, is:

Strength Ratio

• The matrix strength ratio, SRm, is:

Look up more details

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LaRC02 failure analysis (2D), Simcenter 3D 2021.1 Series

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Davila, C.G., Jaunky, N., and Goswami, S., “Failure Criteria for FRP Laminates in Plane Stress”, 44

th

AIAA/ASME/ASCE/AHS Structures, Structural Dynamics, and Materials Conference, Norfolk, Virginia, 7–10 April 2003.

Davila, C.G., Jaunky, N., and Goswami, S., “Failure Criteria for FRP Laminates in Plane Stress”, 44

th

AIAA/ASME/ASCE/AHS Structures, Structural Dynamics, and Materials Conference, Norfolk, Virginia, 7–10 April 2003.

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